The bottom of the glove box door has a long pin for a hinge. There is a spring on that pin. Check and make sure it is intact. If so, remove the glove box door and lube the hinge with some WD-40 and work it back and forth. Try that and see if it gets better!
1966 Impala convertible
1966 Caprice 4dr.
For 45+ years the spring has been in a compressed position with the door closed and developed a memory. A simple fix is to take a nut like a 1/4 inch and pry the center “nose” of the spring up with a small screw driver and then slide the little nut under the nose. This increases the force the spring is able to put on the door.
The most important, and always overlooked, part of opening all glovebox doors of the 60’s & 70’s are those dumb little rubber snubbers. They flatten out over the years, are easily replaced, and the tiny bit of new rubber actually gives the door the push it needs to pop open. Suitable replacements are available at every auto parts chain store in the Motormite-Help-Dorman parts line.